Banks and Bank Accounts
Before you arrive in Dubai DAA will send you a document called Responsibilities As a New Hire, which details some of things you must do, including getting a Dubai bank account so that your salary can be deposited. Once you arrive in Dubai begin the paperwork to obtain a local bank account.

Most banks will open an account before your Residence Visa process is complete. Upon arrival in Dubai obtain a No Objection Letter from the DAA Account’s Department (if you already have your Residence Visa) or from the Superintendents’ Office (if your visa is still in process). Select a bank, possibly from the list below.

Note: While most banks have a branch or counter at MOE (Mall of the Emirates) to obtain cash, some will only have an ATM machine. You may need to travel to the bank itself in order to set up the initial account and then after that you can withdraw money at the Mall. Ask at the MOE customer service desk for ATM locations.

HSBC has most international banking facilities and services including online banking and telegraphic transfers. Make sure you bring the BSB numbers and routing numbers of the accounts so that you can arrange for money transfers. There is one type of account which allows you onefree transfer per month so make sure you ask about it when you sign up. There is a small branch in the MOE that will open accounts for you but they will not deal with cash.
I use HSBC and have not had any problems in 4 years. Knock on wood! I hear others have had problems.
I had HSBC last year and had many problems which couldn't be resolved at MOE - had to travel to Jebel Ali or Bur Dubai and it was a pain. Lots of problems with their ATM machines, took a month to get my ATM card...Basically, their MOE office is a sales center intended to set up new accounts.
Lloyds of London some disagreement about this one:“Don’t use Lloyd’s bank. There isn’t a decent bank that I’ve heard of in all Dubai. Horror stories all around!” versus “ Lloyd's Bank Al Wasl across from Safa Park was voted best International Bank.”
ADCB - good loans for cars
Emirates NBD 24 free international transfers a year, good loans for cars, will allow you to open bank account before visas, etc.
We also inquired about setting up a savings account at Emirates NBD and they told us that U..S. citizens aren't allowed to have interest-bearing accounts in the UAE, but no one at other banks seemed to know anything about this.
Masreq bank
We use Mashreq and they are very helpful though their fees are a bit high.
National Bank of Dubai - Transferring to a US account:
The counters on the first floor of LuLu’s Hypermarket (near school) will transfer cash for 60 dirhams (US$15). You can fill out the paperwork once and then present a card after that which makes it easy.

Money Transfers
We recently found out (by accident) that it actually costs about $30 USD total to transfer money from Al Ansari and other currency exchange counters, and even some banks. They charge 45 or 60 dhs up front and then send your money through an intermediary bank that takes another $15 - $18 USD.